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Theorem mlaconj2 846
 Description: For 5GO proof of Mladen's conjecture. Hypothesis is 5GO law consequence.
Hypothesis
Ref Expression
mlaconj2.1 ((((a1 (ab)) ∩ ((ab) →1 ((ab) ∪ c))) ∩ ((((ab) ∪ c) →1 c) ∩ (c1 (ab)))) ∩ ((ab) →1 a)) ≤ (ac)
Assertion
Ref Expression
mlaconj2 ((ab) ∩ ((ac) ∪ (bc))) ≤ (ac)

Proof of Theorem mlaconj2
StepHypRef Expression
1 mlaconj 845 . 2 ((ab) ∩ ((ac) ∪ (bc))) ≤ ((((a1 (ab)) ∩ ((ab) →1 ((ab) ∪ c))) ∩ ((((ab) ∪ c) →1 c) ∩ (c1 (ab)))) ∩ ((ab) →1 a))
2 mlaconj2.1 . 2 ((((a1 (ab)) ∩ ((ab) →1 ((ab) ∪ c))) ∩ ((((ab) ∪ c) →1 c) ∩ (c1 (ab)))) ∩ ((ab) →1 a)) ≤ (ac)
31, 2letr 137 1 ((ab) ∩ ((ac) ∪ (bc))) ≤ (ac)
 Colors of variables: term Syntax hints:   ≤ wle 2   ≡ tb 5   ∪ wo 6   ∩ wa 7   →1 wi1 12 This theorem was proved from axioms:  ax-a1 30  ax-a2 31  ax-a3 32  ax-a4 33  ax-a5 34  ax-r1 35  ax-r2 36  ax-r4 37  ax-r5 38  ax-r3 439 This theorem depends on definitions:  df-b 39  df-a 40  df-t 41  df-f 42  df-i1 44  df-i2 45  df-le1 130  df-le2 131  df-c1 132  df-c2 133 This theorem is referenced by: (None)
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